Modern polishing technology can provide surfaces with waviness and roughness in the sub-nanometer and Angstrom range. Examples of devices having surface waviness and surface roughness in the foregoing ranges include super-polished optics, magnetic disk substrates, and semiconductor wafers. While the roughness measurements are typically carried out with interference microscopes with high resolution and measurement fields up to a few mm, the waviness measurements tend to require larger measurement fields, e.g., in the tens of mm.
In some cases, the topography measurement of these super-smooth surfaces presents a challenge for the commonly-used interferometers, where the test surface is generally compared to a reference surface inside the interferometer. For the contribution of the interferometric reference surface to be insignificant in the measurement, the roughness and/or waviness of the reference surface topography should be well below that of the test surface, which is difficult to achieve in the example devices mentioned above. Presently, the reference surface topography is determined in a sequence of calibration measurements, and then subtracted from the test surface measurement. However, this procedure may require significant calibration effort. Furthermore, a slight instability in the interferometer can create a shift between the calibration map and the actual measurement error, such that the reference subtraction from the measurement is no longer complete. Frequent recalibrations may be required, especially in the presence of small localized defects and features with significant high-spatial frequency content on the reference surface.
To address one or more of the foregoing problems, interferometric configurations have been described that employ a reference beam where no physical surface is in sharp focus on an interferogram detector of the interferometer (see J. Krug, J. Rienitz, G. Schulz, “Contributions to Interference Microscopy”, Hilger & Watts, London 1964; U. Gerhard, “Erfahrungen mit dem Tripelspiegel-Auflichtinterferenzmikroskop”, Feingeraetetechnik 16, 505 (1967); and U.S. Pat. No. 4,983,042, each of which is incorporated herein by reference in their entirety). In such a configuration, the plane in the reference beam optically conjugate to the interferogram detector is called a virtual reference surface. As opposed to other interferometer configurations (e.g., Michelson, Linnik, or Fizeau), there is no real, physical surface in the conjugate plane. Hence if an extended, spatially incoherent light source is used in this type of interferometer, small defects and roughness on all real surfaces in the reference beam appear blurred on the interferogram detector, and their effects on the interferometric measurement are much reduced or eliminated. Conjugate points and planes are discussed, for example, in Optics, 2nd Edition, by Eugene Hecht, Addison Wesley Publishing Co. (1987), pp. 128-130 and Fundamentals of Optics, 4th edition, by F. Jenkins, H. White, McGraw Hill Book Company, New York 1976, pp. 47, 48, 62.